A. The quote should describe all of the work to be done in detail, including design, installation and verification of operation upon completion. If specific standards to be met are a requirement, then those should be spelled out in the quote, as well as the method of verifying compliance with those standards. The fact that a Manuals J, D, S, T & Z (z if zoned) have been used in the design should be stated. Any omission of such manuals should be cause to disqualify the company from the work.
B. Verification of installation practices can be done different ways but it all adds up to the same thing. Airflow should first be verified under a specific set of conditions, such as wet or dry coil. Balance of the system would normally be done using a flow hood at each supply outlet and return grille. Proper refrigerant charge (for AC or HP) should be verified using both SC and SH as references and charging with the appropriate method for the equipment installed.
You didn't state in your post what type of equipment is to be attached to the duct system. If it's a gas furnace, further testing should be accomplished to verify gas pressures, combustion efficiency as well as airflow in both heating and/or cooling if appropriate. If by some chance it's and oil furnace, further tests of oil pump pressure, exhaust smoke and draft should also be included. Full set-up of any thermostats in the project should be accomplished as well and all design, installation, maintenance and service paperwork, including manuals, should be left on scene in good condition. If there are any rebates due, the installing company should supply all necessary supporting documents as required to qualify the equipment for those rebates.
If YOU want change, YOU have to first change.
If you are waiting for the 'other guy' to change first, just remember, you're the 'other guy's' other guy. To continue to expect real change when you keep acting the same way as always, is folly. Won't happen. Real change will only happen when a majority of the people change the way they vote!